Section 27: Problem 4 Solution
Working problems is a crucial part of learning mathematics. No one can learn topology merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.
James R. Munkres
Given
:
is a continuous function in
that maps a connected space into
, therefore, the image is a connected subspace of
that includes
. This implies that it is either
(
) or uncountable.